As described in U.S. Pat. No. 6,737,841 to Wrathall, closed loop negative feedback systems are commonly employed in linear integrated circuits. For instance, switching regulators use a feedback loop to monitor the output voltages in order to provide regulation. To ensure stability in any closed loop system, the Nyquist Criterion must be met. The Nyquist Criterion states that a closed loop system is stable if the phase shift around the loop is less than 180 degrees at unity gain. Typically, a compensation circuit is added to a feedback loop to modulate the phase shift of the feedback loop to obtain stability. For example, as shown in FIG. 1, a traditional switching regulator 100 comprises a controller 102 and an LC filter 104. In the controller 102, an output control logic 108 drives a switching transistor 106 according to an input voltage VIN and an output of a comparator 114, in order to generate a switching voltage VSW for the LC filter 104 to further generate a regulated output voltage VOUT. The output voltage VOUT is divided by voltage divider composed of resistors R1 and R2 to produce a voltage VR, and an error amplifier 112 compares the divided voltage VR with a reference voltage VRef so as to produce an error output for the comparator 114. The feedback control loop of the controller 102 operates to regulate the output voltage VOUT based on the error output of the error amplifier 112 so that the divided voltage VR equals the reference voltage VRef. The frequency response of a linear circuit can be characterized by the presence of “poles” and “zeros”. Generally speaking, a pole provides a phase shift of −90 degrees and a zero provides a phase shift of +90 degrees. Any person skilled in the art should understand that the error amplifier 112 in the switching regulator 100 has a pole and a zero, and the LC filter 104 provides double-pole. FIG. 2 is a plot of the loop gain magnitude vs. frequency in log scale for the switching regulator 100 of FIG. 1 without any compensation. As shown in FIG. 2, without compensation, the effect of the double-pole in the LC filter 104 causes a large loss in the loop gain such that the phase shift at unity gain is equal to or greater than 180 degrees. Therefore, the feedback control loop of the uncompensated switching regulator 100 of FIG. 1 is unstable unless the gain is substantially reduced.
As shown in FIG. 1, to compensate the double-pole of the LC filter 104 for a stable switching regulator 100, conventionally, a capacitor 110 (typically referred to as a “zero capacitor”) is connected in parallel to the resistor R1 of the voltage divider. The capacitor 110 introduces a zero-pole pair in the feedback loop, and the location (or frequency) of the zero-pole pair is determined by the resistance of the voltage divider and the capacitance of the zero capacitor 110. Here, the operation of the zero capacitor 110 ensures that the phase shift is less than 180 degrees near unity gain. FIG. 3 is a plot of the loop gain magnitude vs. frequency in log scale for the switching regulator 100 of FIG. 1 incorporating the zero capacitor 110. From the circuit shown in FIG. 1, it is known that the capacitor 110 provides the zeroZero=1/(C×R1),  [Eq-1]where C is the capacitance of the zero capacitor 110, and the LC filter 104 has the polePole=[1/(C×R1)]×(VOUT/VR).  [Eq-2]Thereupon, the ratio of the pole to zero is limited to VOUT/VR.
U.S. Pat. No. 6,737,841 to Wrathall provides a zero generating circuit, which uses a gain amplifier to improve the ratio of the pole to zero.
There has been also proposed an amplifier circuit with internal zeros to compensate the double-pole of the LC filter 104 in the switching regulator 100 of FIG. 1. For example, a conventional amplifier circuit 200 with internal zeros is shown in FIG. 4, which comprises a differential input pair composed of voltage-controlled current sources 210 and 212 to generate currents I1 and I2 according to input voltages VN and VP, two current mirrors 202 and 204 to mirror the currents I1 and I2 to generate currents I3=N×I1 and I4=P×I2 respectively, and a further current mirror 206 to mirror the current I3 to determine a current I5=M×I3=N×M×I1, where N×M=P. In the case of VN=VP, there will have the result of I1=I2, and therefore I4=I5. In this case, no current is sourcing to or sinking from the load circuit which is represented by serially connected resistor Rcomp and capacitor Ccomp. In the case of VN≠VP, resulting in a difference between the currents I4 and I5, a non-zero voltage Vout is generated. The network of the resistor Rcomp and the capacitor Ccomp provides a polePole1=1/(2×π×ro×Ccomp),  [Eq-3]where ro is the output impedance of the amplifier circuit 200, and a zeroZero1=1/(2×π×Rcomp×Ccomp).  [Eq-4]Moreover, a zero generating circuit 208 is connected between the voltage-controlled current sources 210, 212 and a bias current source 214 to further provide a zero. The zero generating circuit 208 comprises a zero resistor Rzero1 connected between the voltage-controlled current source 210 and the bias current source 214, another zero resistor Rzero2 connected between the voltage-controlled current source 212 and the bias current source 214, and a zero capacitor Czero connected between the voltage-controlled current sources 210 and 212. Assuming that the resistance Rzero1 is equal to the resistance Rzero2, the network of the zero capacitor Czero and the zero resistors Rzero1 and Rzero2 provides a second zeroZero2=1/(2×π×Rzero1×2×Czero).  [Eq-5]FIG. 5 shows the frequency response of the amplifier circuit 200 with the parameters Rcomp=100 KΩ, Rzero1=Rzero2=230 KΩ, Ccomp=1 nF, and Czero=20 pF. In FIG. 5, the curve 216 represents the gain and the curve 218 represents the phase. As the curve 216 indicates, at the pole Pole1, i.e. 10 Hz, the gain begins to decrease, and until 1 KHz, the zero Zero1 counteracts the pole Pole1 such that the gain becomes stable. Then, at 10 KHz, due to the zero Zero2, the gain begins to increase. Though a switching regulator employing such amplifier circuit 200 eliminates the need of extra components to compensate the double-pole of the LC filter, the amplifier circuit 200 will bring significantly increased gain at high frequency and is therefore disadvantageous in controlling high-frequency noise.
Hence, a need exists for an amplifier circuit with internal zeros to facilitate controlling high-frequency noise.